Help Robert with His Linear Algebra Problem

In summary, Bob was stuck on a linear algebra problem and asked for help on this site. He was told that there might be two solutions to the problem and that he should figure out what s and t are.
  • #1
Bob19
71
0
HELP !: Linear Algebra (I'm stuck)

Hello my name is Robert and I was referred to this site by a guy from my linear algebra class.

The reason for me written to You is because I'm stuck with a linear algebra problem.

Therefore I hope You Guys can give me a hint.

I have an assignement where I am suppose to build a cubic polynomial of degree 3 using some conditions.

Here are the conditions:

p1(-2) = 2 and p'(-2) = 0 p2(4) = 6 and p2'(4) = 0

p1(0) = p2(0) and p1'(0) = p2'(0)

I know I need to construct the polynomial, but my College Professor that polynomials must be written factorized.

e.g.

p(x) = (s+t) x^3 + (s+t) x^2 + sx +t

I would very much appreciate if any of You Guys could give a hint on how to write a cubic polynomial in the for which my Professor asks.

Thanks :-)

Bob
NY
 
Last edited:
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  • #2
Well, based on other, similar, questions that are flying around, I would guess, that we're looking at two cubic polynomials (rather than one which you mention in your post).

An easy way to deal with this type of excercise is to write out the cubic with variables as coefficients i.e.
[tex]p_1(x)=a_1x^3+b_1x^2+c_1x+d_1[/tex]

Then write out the derivatives you have in your equations:
[tex]p_1'(x)=3a_1x^2+2b_1x+c_1[/tex]

and then plug them into your equations:
[tex]2=p_1(-2)=a_1(-2)^3+b_1(-2)^2+c_1(-2)+d_1[/tex]

This will produce a system of equations in the coeficients.

P.S. Since there are only 6 equations, but 8 unknowns, there will be more than one solution.
P.P.S. Cubic Polynomial and Polynomial of degree 3 mean the same thing.
 
  • #3
Hi Nate,

How do I then write it out in the form that my professor wants Us too ??

Best Regards,

Robert

NateTG said:
Well, based on other, similar, questions that are flying around, I would guess, that we're looking at two cubic polynomials (rather than one which you mention in your post).

An easy way to deal with this type of excercise is to write out the cubic with variables as coefficients i.e.
[tex]p_1(x)=a_1x^3+b_1x^2+c_1x+d_1[/tex]

Then write out the derivatives you have in your equations:
[tex]p_1'(x)=3a_1x^2+2b_1x+c_1[/tex]

and then plug them into your equations:
[tex]2=p_1(-2)=a_1(-2)^3+b_1(-2)^2+c_1(-2)+d_1[/tex]

This will produce a system of equations in the coeficients.

P.S. Since there are only 6 equations, but 8 unknowns, there will be more than one solution.
P.P.S. Cubic Polynomial and Polynomial of degree 3 mean the same thing.
 
  • #4
You should be able to figure out what [itex]s[/itex] and [itex]t[/itex] are if you have the polynomial's coefficient.
 
  • #5
I got the coefficients, but don't know how to use them to write the polynomial is desired form ??

Bob



NateTG said:
You should be able to figure out what [itex]s[/itex] and [itex]t[/itex] are if you have the polynomial's coefficient.
 
  • #6
hello Bob

you should have a look at the recent questions asked in this forum i think this same question was recently asked by Mathman23 have look at what was discussed in there

take care

Steven
 

What is linear algebra?

Linear algebra is a branch of mathematics that deals with operations on vectors and matrices. It involves solving systems of linear equations, finding eigenvalues and eigenvectors, and studying vector spaces and linear transformations.

What is Robert's linear algebra problem?

Robert's linear algebra problem is a specific mathematical question or exercise related to the principles and concepts of linear algebra. It could involve solving a system of equations, finding the inverse of a matrix, or applying linear transformations to a set of vectors.

How can I help Robert with his linear algebra problem?

First, it is important to understand the specific problem that Robert is struggling with. Then, you can offer guidance, explain the relevant concepts, and provide step-by-step instructions on how to solve the problem. It may also be helpful to provide additional resources or practice problems for Robert to work on.

Why is linear algebra important?

Linear algebra has numerous applications in various fields, including physics, engineering, computer science, and economics. It provides a powerful tool for solving complex problems involving multiple variables and equations. Additionally, many modern technologies, such as machine learning and computer graphics, rely heavily on linear algebra.

Are there any tips for mastering linear algebra?

Practice is key when it comes to mastering linear algebra. It is important to understand the underlying concepts and principles, rather than just memorizing formulas. Additionally, breaking down problems into smaller, more manageable steps can make them easier to solve. Collaborating with others and seeking help when needed can also be beneficial.

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